Atomic force microscopy and its derivatives have become a very potent tool in the exploration of new materials and processes. Their use has become of critical importance for the semiconductor industry. A new technique has emerged which combines the power of atomic force microscopy and magnetic resonance. It is destined to have a tremendous impact on the science of metrology as did its older cousin, magnetic resonance imaging. This new technique is known as magnetic resonance force microscopy (MRFM).
Magnetic resonance force microscopy is a well-studied technology capable of detecting the magnetic resonance of a small number of spins and, potentially, a single spin of an electron or nucleus [1, 2, 3]. The method is a natural extension of atomic force microscopy whereby the deflection of an ultra sensitive cantilever is used to monitor minute pressure changes associated with magnetic resonance. The high sensitivity of these measurements is a result of the advances in nanotechnology and optical interferometry, which have led to spectacular results. Modem optical interferometry is capable of sub-angstrom deflection measurements, which now, in combination with ultra-sensitive cantilevers, make force measurements below 10xe2x88x9217 newtons per root Hz feasible.
In magnetic resonance force microscopy, a tiny, micron-sized spherical magnet is attached to the cantilever. Because of its small size the magnet produces astronomically large field gradients (up to 44000 T/m). In this high-gradient environment, magnetic resonance sets up a slight change of pressure between the magnet and the sample, and this pressure shows up in the cantilever deflection. The deflection can be enhanced by periodically exciting the resonance at a rate matching the resonance frequency of the cantilever.
The sensitivity of the force measurement is dependent on the properties of the cantilever: the softer the cantilever, the greater the force sensitivity. Great strides have been made in making ultra thin cantilevers having a low force constant [4]. The force on a cantilever is related to the deflection by the familiar formula F=kx, where F is the force, k is the spring constant, and x is the deflection. The force sensitivity (in meters/newton) is inversely proportional to the spring constant, so that a low force constant produces high sensitivity.
Soft cantilevers are difficult to manufacture. They tend to curl up and special materials are required to keep them stiff enough to remain straight. This is a difficult technology that only a few groups have mastered [4].
The cantilever serves several purposes.
1) It holds the magnet in place and allows it to be positioned.
2) It provides some horizontal/lateral x-y stability for the magnet
3) It provides a surface from which to reflect light for interferometer measurements.
4) It provides a mechanical resonator which enhances deflection.
5) It provides a linear force constant in the z-direction, allowing forces to be calibrated in the z-direction.
As cantilevers become thinner and thinner they become less relevant. Sidles and others have shown that it is best in some instances to couple the cantilever to a control coil and control system that can be manipulated to adjust the overall damping and resonance frequency. (Soft cantilevers may have too narrow a Q for practical applications). This requires active feedback from the interferometer to a torque control coil [5].
Another approach is to eliminate the cantilever entirely. This is the subject of the proposed invention. The cantilever is replaced with a field control substrate, forming a xe2x80x9cvirtual cantileverxe2x80x9d. All the features of a cantilever can be obtained using a xe2x80x9cvirtual cantileverxe2x80x9d. The virtual cantilever is comprised of xe2x80x9cfield springsxe2x80x9d or potential wells set up by magnetic fields and/or electric fields. In this concept, the magnet or magnetization is levitated by electromagnetic fields above the surface of the sample. Attached to the magnet is a reflective surface for optically monitoring its height. This combination of magnet and reflective surface, which is herein named a birdie, floats freely above the sample and responds to the local forces. Since the birdie is free-standing and not mechanically bound to any cantilever arm, it has unprecedented force sensitivity. This is a key advantage when probing to detect magnetic resonance from a single electron or nucleus.
There are other advantages to cantilever-free operation. The fact that the birdie and its associated magnetic fields can be rotated or moved by command can potentially open up different magnetic resonance techniques. It may also be easier to fabricate and handle a field control substrate than an ultra-sensitive cantilever.
Levitation is not a revolutionary concept, but doing it at the nano-level is novel. The present inventor has much experience levitating magnetic objects at the macroscopic level using superconducting magnets and control coils. There are a variety of schemes available, including full active magnetic control, the inclusion of passive diamagnetic materials and superconductors (type I and type II), and even electrodes for electric field control. At this stage of development it is too early to define the optimal configuration required for levitation at the microscopic level. For purposes of illustration, a baseline approach is described using active magnetic field control. Other controls can be added later as required by the application.
The cantilever-free approach is a generalized approach and should have applications beyond MRFM in other force microscope instrumentation.